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Chinese Physics B 2010年第7期19卷 238-244页

作者：石鹏曹国威李永平 Department of Optics and Optical Engineering University of Science and Technology of China

Two physical interpretations of chirp transform related to Fresnel diffraction and wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.

关键词： chirp transform Fresnel diffraction wigner distribution function fractional Fourier transform

The wigner distribution function of a super Lorentz–Gauss SLG_(11) beam through a paraxial ABCD optical system

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Chinese Physics B 2013年第10期22卷 272-280页

作者：周益民周国泉 School of Sciences Zhejiang Agriculture & Forestry University

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.

关键词： wigner distribution function super Lorentz-Gauss beam paraxial ABCD optical system

A new finite-dimensional thermal coherent state and its wigner distribution function

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Chinese Physics B 2011年第1期20卷 371-376页

作者：孟祥国王继锁梁宝龙 Department of Physics Liaocheng University College of Physics and Engineering Qufu Normal University

This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal wigner operator in the thermal entangled state representation, the wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its wigner function.

关键词： new finite-dimensional thermal coherent state thermal entangled state representation wigner distribution function

Fractional Fourier transform of flat-topped multi-Gaussian beams based on the wigner distribution function

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Chinese Physics B 2005年第6期14卷 1130-1135页

作者：吴平吕百达陈天禄 DepartmentofAppliedPhysics SouthwestJiaotongUniversityChengdu610031China InstituteofLaserPhysicsandChemistry SichuanUniversityChengdu610064China

By using the wigner distribution function, the fractional Fourier transform (FRFT) of flat-topped multi-Gaussian (FTMG) beams is studied. Analytical expressions for the intensity distribution, beam width, far-field divergence angle,M2 factor and K parameter of FTMG beams are derived. The influence of fractional order on transformation properties of FTMG beams in the FRFT plane is illustrated with numerical examples.

关键词： wigner distribution function flat-topped multi-Gaussian beam fraction Fourier transform

Representation of the wigner distribution function for light beams passing through apertured optical systems

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Representation of the Wigner distribution function for light...

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

Photonics Asia 2004:Information Processing and Data Storage

作者： Daomu Zhao*a, Haidan Maoa, Dong Suna, Zhangrong Meib,a, Linfei Chena, Shaomin Wanga a Department of Physics, Zhejiang University, Hangzhou 310027, China b Department of Physics, Huzhou Teachers College, Huzhou 313000, China

By introducing a method that a hard-edged aperture function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of wigner distribution

关键词： wigner distribution function Gaussian beam aperture ABCD optical systems

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Chinese Physics B 2022年第5期31卷 334-339页

作者： Xiaoyan Zhang Jisuo Wang Lei Wang Xiangguo Meng Baolong Liang Shandong Provincial Key Laboratory of Laser Polarization and Information Technology School of Physics and Physical EngineeringQufu Normal UniversityQufu 273165China Shandong Provincial Key Laboratory of Optical Communication Science and Technology School of Physical Science and Information EngineeringLiaocheng UniversityLiaocheng 252059China School of Physics and Electronic Engineering Heze UniversityHeze 274015China

Two new photon-modulated spin coherent states(SCSs)are introduced by operating the spin ladder operators J±on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution,second-order correlation function,photocount distribution and negativity of wigner *** results show that the photocount distribution is a Bernoulli distribution and the wigner functions are only associated with two-variable Hermite *** with the ordinary SCS,the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j,which means that the nonclassicality can be enhanced by selecting suitable parameters.

关键词： the photon-modulated spin coherent state nonclassicality photocount distribution wigner distribution function

wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

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Chinese Physics B 2012年第8期21卷 234-240页

作者：朱开成李绍新唐英郑小娟唐慧琴 School of Physical Science and Technology Central South University Physical Staff Room Guangdong Medical College

A new kind of quantum non-Gaussian state with a vortex structure, termed a Bessel-Gaussian vortex state, is constructed, which is an eigenstate of the sum of squared annihilation operators a2 ＋ b2. The wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that a quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.

关键词： wigner distribution function quantized vortex state quantum non-Gaussian state

The wigner function and phase properties of superposition of two coherent states with the vacuum state

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Chinese Physics B 2010年第7期19卷 268-275页

作者：王月媛王继成刘树田 Department of Physics Harbin Institute of Technology Key Laboratory for Advanced functional Materials and Excited State Process of Heilongjiang Province School of Physics and Electronic EngineeringHarbin Normal University

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient a, it can generate a variety of nonclassical states.

关键词： coherent states vacuum state wigner distribution function phase properties

Decoherence of elliptical states in phase space

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Chinese Physics B 2011年第5期20卷 6-11页

作者：王月媛刘正君廖庆洪王继成刘树田 Department of Physics Harbin Institute of Technology Key Laboratory for Advanced functional Materials and Excited State Process of Heilongjiang Province School of Physics and Electronic EngineeringHarbin Normal University

The effects of decoherence on elliptical states which concern the quantum superposition of N coherent states on an ellipse in the a plane are studied. The characteristic decoherence times are determined. The evolutions of the wigner functions associated with these states are investigated theoretically and the losses of nonclassicality as a result of decoherence are discussed. The result shows that the decoherence of elliptical states is slower than circular states relying on the number of coherent states and the amplitude, and the constructed states have a higher resilience to losses.

关键词： elliptical states wigner distribution function decohercnce

wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

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Chinese Journal of Lasers 1999年第2期 72-77页

作者： LIU Zhongyong FAN Dianyuan (Shanghai Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences, Shanghai 201800, China)

１ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｒｅｃｅｎｔｙｅａｒｓｆｒａｃｔｉｏｎａｌＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍ（ＦＲＴ）ｈａｓｂｅｎａｔｒａｃｔｅｄｍｕｃｈａｔｅｎｔｉｏｎｉｎａｗｉｄｅｆｉｅｌｄｏｆａｐｐｌｉｃａ... 详细信息

１ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｒｅｃｅｎｔｙｅａｒｓｆｒａｃｔｉｏｎａｌＦｏｕｒｉｅｒｔｒａｎｓｆｏｒｍ（ＦＲＴ）ｈａｓｂｅｎａｔｒａｃｔｅｄｍｕｃｈａｔｅｎｔｉｏｎｉｎａｗｉｄｅｆｉｅｌｄｏｆａｐｐｌｉｃａｔｉｏｎｓ．ＴｈｅｆｉｒｓｔＦＲＴ...

关键词： wigner distribution function fractional Fourier transform first order optical system reciprocally symmetric optical system